--90e6ba6e87b20b4a0c04987afb8d
Content-Type: text/plain; charset=ISO-8859-1
>
>
>>
> I can't imagine where you got the idea that a nul is less than minus
> infinity. Mathematically, a null is basically undefined as in dividing by
> zero. I have no idea what your use of this is, but mathematically you are in
> the wrong pew.
>
> Everett L.(Rett) Williams II
>
>
where i get that from is this:
when you look at a graph of 1/x lim(+x->0) +infinity; lim(-x->0) -infinity;
(that's also what i learned in my calculus courses) so 1/0 (kind of) has a
value depending on which direction you approach 0 from.
null on the other hand - as you said - is undefined. and when you compare
null to ANY value - even neg infinity - you still have a value on one hand
and nothing on the other. and while it sucks, having -infinity dollars you
have SOME value (to bill collectors) and having nil dollars you have no
value (to anyone). that example is kind of bad cause nil 0, but that's
not my point. if you read some of the papers i provided in the first post
(esp. this one:
http://www.tondering.dk/main/index.php/surreal-numbers) part of the
definition of a surreal number is a comparison with nil. the first surreal
number { nil | nil } is defined as 0, and the second generation { { nil |
nil } | nil } is defined as 1 and { nil | { nil | nil } } is -1 ( commonly
written simply as { | }; { 0 | } and { | 0 }. and { 0 | 0 } is not
well-defined in the definition of surreal numbers )
so while it might not make sense to most people (indeed, i'm working on
stretching my brain around all this) this is the definition i'm working
with, and i'm not going to argue with math phd's
as for the utility of it all? surreal numbers are commonly used in game
theory. though the reason why i'm building this class is not for utility,
but as an exercise in 'can i do this?' there are some problems that may
come up later i'm going to have to find some way to deal with ( sets of
infinite objects being one of them, surreal numbers being cool enough that
it gives meaning to things like infinity + 6 and infinity/2 ).
so i hope i answered your question and maybe taught you something.
hex
p.s. i still might be mostly wrong, but again, i'm trusting the articles i'm
reading. maybe i should have one of those cool math-like people look at
this?
--90e6ba6e87b20b4a0c04987afb8d--